Remark 4.7 It is worth mentioning that if we assume that \(G\rightrightarrows M\)  is proper and étale then we may prove that Morse Lie groupoid morphisms on \(G\rightrightarrows M\)  are dense without requiring that \(M\)  is compact. We only have to use the local description of such a Lie groupoid around any point provided by [1]} together with Proposition REF  and Hepworth's ideas in the context of orbifolds as we did in Theorem REF . In this case, the existence of the compact sets \(K_\alpha \)  containing \(\textnormal {Crit}(f|_{U_\alpha })\)  is for free. See [2]} for specific details.

